FlowMM is a generative model designed to predict stable crystal structures and propose novel compositions along with their stable structures. It generalizes Riemannian Flow Matching to account for the symmetries inherent to crystals, including translation, rotation, permutation, and periodic boundary conditions. FlowMM uses a Continuous Normalizing Flow to estimate symmetric distributions over fractional atomic coordinates and the unit cell, enabling efficient and flexible learning of crystal structures. It outperforms diffusion models in terms of integration steps and efficiency, and is validated with quantum chemistry calculations, showing it is approximately three times more efficient at finding stable materials. FlowMM is tested on two realistic datasets and two simplified unit tests, demonstrating competitive or state-of-the-art performance on standard metrics. It also shows comparable stability to other methods while being significantly faster at inference time. FlowMM is able to generate materials with stable structures, as determined by their energetic distance to the convex hull, and is competitive with diffusion models on most metrics, but significantly outperforms them on several Wasserstein distance metrics. FlowMM is also more efficient in terms of integration steps and is able to generate materials with a distribution of unique elements per material that closely matches the MP-20 dataset. The model is evaluated on both CSP and DNG tasks, showing strong performance on all proxy-metrics. FlowMM is able to outperform DiffCSP in terms of Match Rate with as few as 50 integration steps, representing at least an order of magnitude improvement. FlowMM is also more efficient in terms of integration steps and is able to generate materials with a distribution of unique elements per material that closely matches the MP-20 dataset. The model is evaluated on both CSP and DNG tasks, showing strong performance on all proxy-metrics. FlowMM is able to outperform DiffCSP in terms of Match Rate with as few as 50 integration steps, representing at least an order of magnitude improvement.FlowMM is a generative model designed to predict stable crystal structures and propose novel compositions along with their stable structures. It generalizes Riemannian Flow Matching to account for the symmetries inherent to crystals, including translation, rotation, permutation, and periodic boundary conditions. FlowMM uses a Continuous Normalizing Flow to estimate symmetric distributions over fractional atomic coordinates and the unit cell, enabling efficient and flexible learning of crystal structures. It outperforms diffusion models in terms of integration steps and efficiency, and is validated with quantum chemistry calculations, showing it is approximately three times more efficient at finding stable materials. FlowMM is tested on two realistic datasets and two simplified unit tests, demonstrating competitive or state-of-the-art performance on standard metrics. It also shows comparable stability to other methods while being significantly faster at inference time. FlowMM is able to generate materials with stable structures, as determined by their energetic distance to the convex hull, and is competitive with diffusion models on most metrics, but significantly outperforms them on several Wasserstein distance metrics. FlowMM is also more efficient in terms of integration steps and is able to generate materials with a distribution of unique elements per material that closely matches the MP-20 dataset. The model is evaluated on both CSP and DNG tasks, showing strong performance on all proxy-metrics. FlowMM is able to outperform DiffCSP in terms of Match Rate with as few as 50 integration steps, representing at least an order of magnitude improvement. FlowMM is also more efficient in terms of integration steps and is able to generate materials with a distribution of unique elements per material that closely matches the MP-20 dataset. The model is evaluated on both CSP and DNG tasks, showing strong performance on all proxy-metrics. FlowMM is able to outperform DiffCSP in terms of Match Rate with as few as 50 integration steps, representing at least an order of magnitude improvement.